Magnetic X-point collapse is investigated using a 2.5D fully relativistic particle-in-cell simulation, with varying strengths of guide-field as well as open and closed boundary conditions. In the zero guide-field case we discover a new signature of Hall-reconnection in the out-of-plane magnetic field, namely an octupolar pattern, as opposed to the wellstudied quadrupolar out-of-plane field of reconnection. The emergence of the octupolar components was found to be caused by ion currents and is a general feature of X-point collapse. The effect was shown to be independent of system size and ion mass and confined to a few ion inertial lengths from the reconnection current sheet. In a comparative study of tearing-mode reconnection, signatures of octupolar components are found only in the out-flow region. It is argued that space-craft observations of magnetic fields at reconnection sites may be used accordingly to identify the type of reconnection. Further, initial oscillatory reconnection is observed, prior to reconnection onset, generating electromagnetic waves at the upper-hybrid frequency, matching solar flare progenitor emission. When applying a guide-field, in both open and closed boundary conditions, thinner dissipation regions are obtained and the onset of reconnection is increasingly delayed. Investigations with open boundary conditions show that, for guide-fields close to the strength of the in-plane field, shear flows emerge, leading to the formation of electron flow vortices and magnetic islands. Asymmetries in the components of the generalised Ohm's law across the dissipation region are observed and inertial components are shown to play a role at the X-point. Extended in 3D geometry, it is shown that locations of magnetic islands and vortices are not constant along the height of the current-sheet. Vortices formed on opposite sides of the current-sheet travel in opposite directions along it, leading to a criss-cross vortex pattern. Similarly to oblique current sheets previously observed in 3D guide-field reconnection studies, vortex-tubes are inclined at the same angle as the magnetic field.

Abstract This thesis examines magnetic reconnection in the solar corona. Magnetic reconnection is the only mechanism which allows the magnetic topology of magnetized plasmas to be changed. Many of the dynamic processes in the Sun's atmosphere are believed to be driven by magnetic reconnection and studying the behaviour of such phenomena is a key step to understanding the reconnection mechanism. In Chapters 1 to 3, we discuss the physical and mathematical framework on which current magnetohydrodynamic reconnection models are based. The aim of the thesis is to investigate theoretical models of magnetic reconnection using variety of analytic and numerical techniques within the theoretical frame work of magnetohydrodynamics (MHD). In Chapter 4 we use a line-tied X-point collapse model for compressible plasmas to investigate the role of viscosity on the energy release mechanism. This model also provides the basis for the investigation of Chapter 5 which explores the impact of Hall currents in the transient X-point energy dissipation. Chapter 6 is concerned with how reconnection is modified in the presence of generalized Ohm's law which includes both Hall current and electron inertia contributions. In contrast to the closed X-point collapse geometry adopted for compressible plasmas previously, we find it more convenient to explore this problem using an open incompressible geometry in which plasma is continually entering and exiting the reconnection region. Specially, we find the scaling of the Hall-MHD system size analytically, rather than numerically as in the X-point problem of Chapter 5. Chapter 7 summarizes the results of investigations in Chapters 4, 5 and 6.